Possible Sqrt Simplification Bug

[Zak V]

Hello,

    I believe I found a bug in how radicals are simplified.  The general idea is that sqrt(x^2)=abs(x), but sage simplifies sqrt(x^2) to x instead, even if x is negative.  I've included a simple example below.  

sage: x = var('x')

sage: assume(x<0)

sage: expr = sqrt(x^2)

sage: simp_expr=expr.simplify_radical()

sage: eqn = expr==simp_expr

sage: print eqn

sqrt(x^2) == x

sage: print eqn.subs(x=-1) #Clearly this is wrong

1 == -1

sage: abs(x).simplify() #However, Sage knows how to deal with abs(x) for x<0

-x

I've never used the Sage Trac system before, so I thought posting this to here might instead might be a good idea.  Hope this is helpful.

Cheers,

Zak

[kcrisman]

For more or less this reason, simplify_radical was removed from simplify_full.  However, it is still useful.  See http://www.sagemath.org/doc/reference/calculus/sage/symbolic/expression.html#sage.symbolic.expression.Expression.simplify_radical for some specifics on exactly what it claims (and doesn't claim) to do.  In particular, one can have arbitrarily long arguments (and we have) about exactly what the underlying Maxima "radcan" really "should" do.  I don't think this counts as a bug, but rather as user beware - simplifications sometimes are indeed simplifications, like x^2/x = x.

Or, if it's because of the assumption, I think that Maxima's simplification methods do not take that into account.   The method simplify() just sends to Maxima and back, and for that it does take it into account.

- kcrisman